# A Test for Comparing Multiple Misspecified Conditional Distributions

*Valentina Corradi* and
*Norman Swanson* ()

Departmental Working Papers from Rutgers University, Department of Economics

**Abstract:**
This paper introduces a conditional Kolmogorov test, in the spirit of Andrews (1997), that allows for comparison of multiple misspecifed conditional distribution models, for the case of dependent observations. A conditional confidence interval version of the test is also discussed. Model accuracy is measured using a distributional analog of mean square error, in which the squared (approximation) error associated with a given model, say model i; is measured in terms of the average over U of E((Fi(u|Zt,Theta-t-plus)-Fo(u|Zt,Theta-o)))^2; where U is a possibly unbounded set on the real line, Zt is the conditioning information set, Fi is the distribution function of a particular candidate model, and F0 is the true (unkown) distribution function. When comparing more than two models, a “benchmark” model is specified, and the test is constructed along the lines of the “reality check” of White (2000). Valid asymptotic critical values are obtained via a version of the block bootstrap which properly captures the e®ect of parameter estimation error. The results of a small Monte Carlo experiment indicate that the conditional confidence interval version of the test has reasonable finite sample properties even for samples with as few as 60 observations.

**Keywords:** block bootstrap; conditional Kolmogorov test; data snooping; misspecified conditional distribution (search for similar items in EconPapers)

**JEL-codes:** C22 C52 (search for similar items in EconPapers)

**Date:** 2003-10-21

**New Economics Papers:** this item is included in nep-ecm

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**Persistent link:** https://EconPapers.repec.org/RePEc:rut:rutres:200314

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